Section vi. flat plates and curved surfaces. at various angles of incidence

Now it was time to compare the theoretical predictions with the results of ex­periment. Kutta did not perform experiments himself but used existing data. The aim was to see if the predicted relation between lift and angle of incidence was correct. The formula for the circulation shows that the circulation increases with increasing angle of incidence, so lift should likewise grow. Kutta worked out two sets of testable results, one for a flat plate, the other for the curved wing. The two predictions are closely related because the flat plate is just the limiting case of the curved plate. The limiting process greatly simplified the formula and permitted a rough comparison with flat-plate data already pub­lished by Duchemin and Langley. The experimental lift was about two-thirds of that predicted by the theory. Kutta declared this “nicht ganz schlecht” (52), which might be rendered as “not too bad.” In his discussion of the flat plate, Kutta also established that the center of pressure will be at a point one-quarter the width of the chord from the leading edge and that, unlike for the curved plate, the position stays the same even though the angle of incidence changes.

Coming now to the curved wing, Kutta used Lilienthal’s own data, which were generated by experiments on a small model of an arc-shaped wing with a sharp leading edge. Because of the sharp leading edge, Kutta thought that friction effects would be dominant so that the leading-edge suction would be damped down or removed. He therefore compared Lilienthal’s measurements with predictions drawn from two different parts of the theoretical analysis. In one case he computed the lift from the general formula showing that the lift = density X velocity X circulation. In the other he used the pressure lift alone (that is, the theoretical lift minus the leading-edge suction). This latter case created a drag because the resultant was tilted backward. On the basis of cer­tain assumptions about the test conditions, Kutta made his predictions for lift and drag for nine different angles of incidence from -9°, through 0°, to +15°. Overall he found that the theoretical predictions of lift were consistently 10 -20 percent higher than those arrived at by observation. Kutta concluded:

Aus der Tabelle scheint also hervorzugehen, dafi fur die untersuchte gewolbte Flache und fur Luftstofiwinkel unter 15° die beobachtete Hubkraft 80-90 Prozent der errechneten ausmacht—was mit dem Umstande, dafi die theore – tischen Vereinfachungen sicher auf zu grofie Zahlen fuhren mufiten, in Uber- einstimmung steht. Auch fur den Stirnwiderstand ergeben sich einigermafien brauchbare Zahlen. (54)

It follows from the table that, for the curved surfaces that were studied, the observed lift force was 80 -90 percent of the calculated value for angles of incidence below 15°—which constitutes agreement given that the theoretical simplifications were bound to lead to numbers that were too high. Even the values for the frontal resistance are reasonably useful.

In other words, the theory fitted the data tolerably well given the approxima­tions that had been made.